Cycle‐factors in oriented graphs

Abstract

AbstractLet be a positive integer. A ‐cycle‐factor of an oriented graph is a set of disjoint cycles of length that covers all vertices of the graph. In this paper, we prove that there exists a positive constant such that for sufficiently large, any oriented graph on vertices with both minimum out‐degree and minimum in‐degree at least contains a ‐cycle‐factor for any . Additionally, under the same hypotheses, we also show that for any sequence with and the number of the equal to 3 is , where is any real number with , the oriented graph contains disjoint cycles of lengths . This conclusion is the best possible in some sense and refines a result of Keevash and Sudakov.